Functions f(x) and g(x) are shown below:

f(x) = 2cos(x)

g(x) = (3)sin(x+pi), a graph of sine function which starts at 0 comma 0 and decreases to the minimum of pi over 2 then increases to the maximum 3 pi over 2 then decreases to 2pi where the cycle repeats.

using complete sentences, explain how to find the maximum value for each function and determine which function has the largest maximum y-value.

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the functions y=sin(x) and y=cos(x) are the standart functions; it means, the period of each is 2π, maximum value is '1', minimum value is '-1'.

Using the properties described above, to find the max. value for the function y=2cos(x): 2*1=2, where 2- the amplitude of the given function, 1- maximum of the standart function;

the max. value for the function y=3sin(x+π): 3*1=3, where 3 - the amplitude of the given function, 1- maximum of the standart function.

For more details see the attached picture.

In other words, common equation for such functions is y=A*sin(ωx+Ф), where A- amplitude, ω - frequency and Ф - initial phase of the given function.

Max. and min. values depend on A, all the points of the function repeat every 2π, including max. and min. values.